1 year, 6 months ago
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Which method of finding the equation a line is the easiest and why?
You can use the point slope form to get a line or you can use slope intercept form. Of course it depends on what is given in the problem, but which method do you find easiest to use? Which is easier to explain to someone who is trying to learn how to find the equation of a line?
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M$1 Answer
I think the calculations are easiest using the slope intercept form, which is y=mx+b, where m is the slope of the line and b is the y intercept. I will solve a problem using both methods to demonstrate why the slope intercept form is simpler.
Example:
Find the equation of the line that passes through the points (3,5) and (1,7)
Slope intercept form: Find the slope first using (y2-y1)/(x2-x1). (7-5)/(1-3) = -1
Use one of the two points and put, x,y and m into the y=mx+b equation
7=(-1)(1)+b
7= -1+b
b=8
now just put m= -1 and b=8 back into the equation to get y= -1x+8
Using the point slope form you still get the slope the same way, so slope is -1
Now you use one of the two points in this equation y-y1=m(x-x1) substituting in for x1 and y1
y-7= (-1)(x-1)
y-7 = -x +1
y= -x+8
What makes the first method slightly easier is you don't have to distribtute, in the second method you do with the -1 and the (x-1). Both methods are fairly simple though.
Example:
Find the equation of the line that passes through the points (3,5) and (1,7)
Slope intercept form: Find the slope first using (y2-y1)/(x2-x1). (7-5)/(1-3) = -1
Use one of the two points and put, x,y and m into the y=mx+b equation
7=(-1)(1)+b
7= -1+b
b=8
now just put m= -1 and b=8 back into the equation to get y= -1x+8
Using the point slope form you still get the slope the same way, so slope is -1
Now you use one of the two points in this equation y-y1=m(x-x1) substituting in for x1 and y1
y-7= (-1)(x-1)
y-7 = -x +1
y= -x+8
What makes the first method slightly easier is you don't have to distribtute, in the second method you do with the -1 and the (x-1). Both methods are fairly simple though.
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